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Day 267: JEE Mains Maths

5 questions. Try each one first, then open its answer.

  1. Question 1

    Conic Sections. Asked once: 1 Feb 2023 (same type asked 4 times) See all 4 of this type

    173
    If the xx - intercept of a focal chord of the parabola y2=8x+4y+4y^{2}= 8x + 4y + 4 is 3 , then the length of this chord is equal to

  2. Question 2

    Matrices. Asked once: 27 Jul 2022 (same type asked 4 times) See all 4 of this type

    64
    Let A=(12−2−5)A =\begin{pmatrix} 1 & 2 \\ - 2 & - 5 \end{pmatrix}. Let α,β∈R\alpha,\beta \in R be such that αA2+βA=2I\alpha A^{2}+ \beta A = 2I. Then α+β\alpha + \beta is equal to -

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  3. Question 3

    Relations and Functions. Asked once: 11 Apr 2023 (same type asked 4 times) See all 4 of this type

    69
    An organization awarded 48 medals in event ' AA ', 25 in event ' BB ' and 18 in event ' CC '. If these medals went to total 60 men and only five men got medals in all the three events, then, how many received medals in exactly two of three events?

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  4. Question 4

    Differential Equations. Asked once: 2021 Paper 25 (same type asked 4 times) See all 4 of this type

    64
    The rate of growth of bacteria in a culture is proportional to the number of bacteria present and the bacteria count is 1000 at initial time t=0t= 0. The number of bacteria is increased by 20%20\% in 2 hours. If the population of bacteria is 2000 after klog⁡e(65)\frac{k}{\log_{e}\left( \frac{6}{5} \right)} hours, then (klog⁡e2)2\left( \frac{k}{\log_{e}2} \right)^{2} is equal to

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  5. Question 5

    Inverse Trigonometric Functions. Asked once: 27 Jun 2022 (same type asked 4 times) See all 4 of this type

    79
    sin⁡−1(sin⁡2π3)+cos⁡−1(cos⁡7π6)+tan⁡−1(tan⁡3π4)\sin^{- 1}\left( \sin\frac{2\pi}{3} \right)+\cos^{- 1}\left( \cos\frac{7\pi}{6} \right)+\tan^{- 1}\left( \tan\frac{3\pi}{4} \right) is equal to:

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